ATOMIC PHYSICS

ATOMIC PHYSICS
1. 1. Structure of the ATOM
-Describe the Rutherford and bohr’s models of the atom.
-Analyze atomic energy levels.
-Discuses the hydrogen energy levels, and derives expressions for the energy levels.
-Perform experiment to determine wavelength in the Balmer series of the hydrogen spectrum.
2. Quantum physics
- Describe failures of classical physics.
- Explain Planck’s quantum theory of blackbody radiation.
- Spectral distribution of black body radiation.
- Explain Einstein’s quantum theory of light.
- Perform experiment to determine the Planck’s constant.
- Account for the photoelectric effect phenomenon.
- Deduce stopping potential threshold frequency and work function of a metal.
- Explain the photo electric effect.
- Deduce de Broglie wave length for electron.
- Discus the wave- particle duality of electron.
- Derive de Broglie’s wavelength for the electron.
- Describe production and uses of x- rays.
- Uses in medicine, industry and in sample analysis.
3. 3. LASER
- Describe production of laser light.
- Explain properties of laser light.
- Distinguish types of lasers.
- Discuss methods of pumping in laser production.
- Identify application of laser light.
4. 4. Nuclear Physics
- Describe the structure of the nucleus.
* Review Rutherford experiment.
- Determine half life and the decay constant (λ) of a radioactive substance.
- Explain the relation of nuclear mass and binding energy.
* Discuss Einstein’s mass energy equation.
* Apply Einstein’s mass energy relation to determine the biding energy of nuclei.
- Identify criteria for stable and unstable nucleus.
* Analyze the neutron and proton ratio and plot N against Z for radioactive elements.
* Establish criteria for stable and unstable nuclei
- Identify uses and hazards of radioisotopes
* Application
* Hazards

- Distinguish between fission and fusion processes
* Meaning of fission and fusion
* Calculate the energy released in a nuclear fission
* Calculate the energy absorbed in nuclear fission
* Describe the application of nuclear fission and fusion
- Describe operation of a nuclease reactor
* Construction and operation of nucleus reactor for safe application
THOMSON’S MODEL OF ATOM
According to Thomson an atom is a positive charged sphere in which the entire mass and
positive charge of the atom is uniform distributed with negative electrons embedded in it as
shown.
The number of electrons is such that their negative charge is equal to the positive charge of the
atom. This atom is electrically neutral.
This model was called Thomson’s plum pudding model because the negatively charge electrons
(the plums) were embedded in a sphere of uniform positive charge (the pudding).
Drawbacks of this Model
1.It could not provide stability to the atom it is because the positive and negative charges are
stationary and will be drawn towards each other, thus destroying the individual negative and
positive charges.
2. It could not explain the presence of discrete spectral lines emitted by hydrogen and other
atoms.
RUTHER FORD’S MODEL OF ATOM
The salient features of this model are
(i)Every atom consist of a tiny central core, called the nucleus which contains all the atom’s
positive charge and most of its mass (99.9%).

(iii) The electrons occupy the space outside the nucleus. Since an atom is electrically neutral
the positive charge on the nucleus is equal to the negative charge on electrons surrounding the
nucleus.
(iv) Electrons are not stationary but revolve around the nucleus in various circular orbits as do
the planets around the sun.
In this way Rutherford provided stability to the atom. It is because the centripetal force required
by the electrons for revolution is provided by the electrostatic force of attraction between
electrons and the nucleus.
e = charge on electron
z =total number of protons in the nucleus
m=mass of the electron
r =distance of electron from the nucleus
v= linear velocity of the electron
Force of attraction between electron and the nucleus is

where Ze is a nuclear charge
The centripetal force required to keep the electron moving in circular path is
Since the atom is stable
Kinetic energy of electron
From equation (1)

Potential energy of electron
Total energy of electron
The total energy of electron in the orbit is negative hence the electron is bound to the positive
nucleus
For hydrogen Atom
For hydrogen atom z= 1. Therefore K. E and P.E OF electron in hydrogen atom are
The total energy of electrons hydrogen atom is

Limitations of Rutherford’s model of atom
1. According to Maxwell’s theory of electromagnetism a charge that is accelerating radiates
energy as electromagnetic waves
The electron moving around the nucleus is under constant accelerating radiates energy as
electromagnetic waves.
- Due to this continuous loss of energy the electrons in Rutherford’s model were bound to
spiral towards the nucleus and fall into it when all of their rotational energy were radiated
- Hence Rutherford’s atomic model cannot be stable while in actual practice, an atom is stable
This shows that Rutherford’s model is not correct
1. During inward spiraling the electron’s angular frequency continuously increases
- As result electrons will radiate electromagnetic waves of all frequency i.e. the spectrum of
these waves will be continuous in nature because these are continuous loss of energy.
- But this is contrary to observation experiments shows that an atom emits line spectra and each
line corresponds to a particular frequency or wavelength.
Rutherford’s model failed to account for the stability of the atom. It was also unable to explain
the emission of line spectra.
BOHR’S MODEL OF ATOM
According to Bohr's atomic model, the revolving electrons in the atom do not emit radiations
under all conditions. They do so under certain conditions as expalined by him in his model.
BASIC POSTULATES OF BOHR’S MODEL OF ATOM
1. The electrons revolve around the nucleus of the atom in circular orbits. The centripetal force
required by electrons for revolution is provided by the electrostatic force of attraction between
the electrons and the nucleus.
2. An electron can revolve only in those circular orbits in which its angular momentum is an
integral multiple of

h= Plank’s constant.
Radius of orbit r
From,
Since n is a whole number only certain value of r is allowed.
Thus according to Bohr, an electron can revolve only in certain orbits of definite radii not in all
these are called stable orbits (stationary orbit)
According to this postulate the angular momentum of the electron does not have continuous
range i.e. the angular momentum of the revolving electron is quantized.
While revolving in stable or stationary orbits the electrons do not radiate energy inspite of
their acceleration towards the centre of the orbit.
- For this reason these permitted orbits are called stable or stationary orbits.
e= charge on electron
m= mass of electron
rn= radius of the nth orbit
vn= velocity of electron in the nth orbit
Z= number of positive charge (protons)
Positive charge on nucleus Ze
RADIUS OF BOHR’S STATIONARY ORBITS

As the centripetal force is provided by the electrostatic force of attraction between the nucleus
and electron.
According to Bohr
Consider equation
Take equation (ii) square it
Take equation (iii) equation (i)
= .

It is clear that n2, radii of the stationary orbits are in ratio 12: 22:32 ………..clearly the
stationary orbits are not equally spaced.
For hydrogen atom
For hydrogen atom z= 1, so that equation become
Now = 0.53 x10-10m
e = electronic charge = (0. 53 x 10-10) metres
Thus the radii of the first, second and third stationary orbits of hydrogen atom are 0.53 Å, 2.12 Å
and 4.77Å respectively.
2. VELOCITY OF ELECTRON IN BOHR’S STATIONARY ORBIT
From equation below, we have

Putting the value of into that equation
It is clear that in other words, electrons move at a lower speed in higher orbits and vice
versa.
For hydrogen atom
Z =1
Then
3. FREQUENCY OF ELECTRON IN STATIONARY ORBIT
The number of revolution completed per second by the electron in a stationary orbit around the
nucleus
Velocity of electron in the orbit

For hydrogen atom
Z = 1
Then,
Frequency of electron in the first orbit of hydrogen atom is n=1, r1=0.53x10-10
m
Electron in first orbit of hydrogen atom will have a frequency of 6.57x 1015revolutions per
second.
4. TOTAL ENERGY OF ELECTRON IN STATIONARY ORBIT
The total energy En of the electron in the nth orbit is the sum of kinetic and potential energy in the
nth orbit.

- The K.E of electron in the nth orbit is
The potential energy of electron in the nth orbit is
Total energy of electron in the nth orbit is
But

Thus as n increases i.e. electron moves to higher orbit, the total energy of the electron increases
i.e. total energy becomes less negative.
For hydrogen atom z=1
Thus the total energy of electron in a stationary orbit is negative which means that the electron is
bound to the nucleus and it is not free to leave the atom.
We can find the total energy of electron in the various orbits of hydrogen atoms as under.
The total energy of electron increases i.e. becomes less negative as the electron goes to higher
orbits
When n→∞ En =0 and the electron becomes free
Ground state/ normal state
This is the state of atom when the entire electrons in it occupies their lowest energy levels as
required by their n and l values.
The energy of an atom is least i.e. largest negative value when n=1 i.e. when electron revolves in
the first orbit.
The energy of hydrogen atom in the ground state is 13.6eV.
Excited state

This is the state of an atom when electrons in an atom occupy energy levels higher than those
permitted by the values of n and l values.
At room temperature most of the hydrogen atoms are in the ground state
If hydrogen atom absorbs energy i.e. due to rise in temperature it may be promoted to one of the
higher orbits (i.e. n=2, 3, 4…..)
The atom is said to be in the excited state.
WAVE LENGTH OF EMITTED RADIATION.
When an electron jumps from a higher orbit (n2) to the lower orbit (n1) the energy difference
between the two orbits is released because the energy of electron in the higher orbit is more than
in the lower orbit. Consider two orbits having principle quantum numbers n2 and n1 where n2>n1
Then energy of electron in the two orbits is given by
As the electron jumps from orbit n2 to n1, energy is released in the form of electromagnetic
radiation.
where
f= frequency of the emitted radiation

The wavelength of the emitted radiation is given by
c=λf
=
This equation gives the wavelength of emitted radiation.
Now,
= = wave number
Wave number
These are the number of waves in a unit length.
For hydrogen atom
For hydrogen atom z = 1

This gives the mathematical formula for the wavelength of radiation emitted by hydrogen atom
when electron jumps from outer orbit to inner orbit.
where
RH is Rydberg constant. The value of RH can be calculated as the value of e, m, h and c are
known
HOW TO CALCULATE THE RYDBERG CONSTANT USING CALCULATOR
From

Clearly, wavelength/frequency of radiation emitted from the excited atom is not continuous.
They have definite value depending upon the values of , and
SPECTRAL SERIES OF HYDROGEN ATOM
Bohr gave a mathematical explanation for the spectrum of hydrogen atom.
The whole hydrogen spectrum can be divided into district groups of lines each group of lines is
called spectral series.
The wavelength of the lines in each group can be calculated from Bohr’s formula

=
The following are spectral series of hydrogen atom
i) Lyman series
ii) Balmer series
iii) Paschen series
iv) Bracket series
v) Pfund series
i) Lyman series
The Lyman series is obtained when electron jump to first orbit n1=1 from outer orbits ( =2, 3,
4…)
Therefore the formula for calculating the wavelength of the lines in this series is,
where
This series lies in the ultraviolet region which is the invisible region.
ii) Balmer series
Therefore the formula for calculating the wavelength of the lines in this series is

where
This series lies in the visible spectrum and was found first of all in the hydrogen series
iii) Paschen series
where
This series lies in the infrared region.
iv) Brackett series
Therefore the formula for calculated the wavelength of the lines in this series is
This series lies in the infrared region.

v) Pfund series
The Pfunds series is obtained when electrons jump to fifth orbit n1 = 5 from outer orbits (n2 =6,
7, 8…..)
where
(n2 =6, 7, 8…..)
This series also lies in the infrared region
ENERGY LEVEL DIAGRAM
Energy level diagram is a diagram in which the total energies of electron in different stationary
orbit of an atom represented by parallel horizontal lines drawn according to some suitable energy
scale
In order to draw energy level diagram of an atom we must know the total energy of electron in
different stationary orbits.
The total energy of an electron in the nth orbit of hydrogen atom is given by
By putting value of n=1, 2, 3….. we can find the total energy of electron in various stationary
orbits of hydrogen atom as
Similarly we can find the total energy of electron in the higher orbits

The table below gives the total energy of electron of hydrogen atom in different stationary orbits.
The energy level diagram of hydrogen atom is shown
below
Total energy of electron in a stationary orbit is represented by a horizontal line drawn to some
suitable energy scale.

(i) The hydrogen atom has only one electron and this normally occupies the lowest level and
has energy of -13.6eV
When the electron is in this level the atom is said to be in the ground state.At room
temperature nearly all the atoms of hydrogen are in ground.
(ii) If hydrogen atom absorbs energy (due to rise in temperature )the electron may be
promoted into one of the higher energy levels
The atom is now said to be in an excited state.Thus when the electron occupies other
than the lowest energy level the atom is said to be in the excited state.
(iii) Once in an excited state the atom is unstable after a short time interval the electron falls
back into the lowest state so that the atom is again in the ground state.
The energy that was originally impacted is emitted as electromagnetic waves.
(iv) The total energy of electron for (n= ) it becomes free of atom.
The minimum energy required to free the electron from the ground state of an atom is
called ionization energy
For hydrogen atom ionization energy is +13. 6eV
(v) The difference between the adjacent energy goes on decreasing as the value of n
increases.
So much so that when n>10 the energy difference is almost zero this is show by
closeness of energy level lines at higher levels.
(vi) Note that region is labeled continuous at energy above zero n= level, the electron is
free from the atom and is at rest
Higher energy represents the translation kinetic energy of the free electron
This energy is not quantized and so all energies above n = are allowed
IMPORTANT TERMS
It is desirable to discuss some important terms much used in the study of structure of atom.
(i) EXCITATION ENERGY
Excitation energy is the minimum energy required to excite an atom in the ground state to
one of the higher stationary state.

Hydrogen atoms are usually in their lowest energy state where n=1
In this state (ground state) they are said to be unexcited.
However if you bombard the atoms with particles such as electron or proto collision can
excite them
In other words a collision may give an atom enough energy to change it from ground state to
some higher stationary state.Consider the case of hydrogen atom we know that = -13.6eV
(ground state = -3.4eV (first excited state) =1.51eV (second excited state) and =0
In order to lift an electron from ground state n =1 to the first excited state n=2 energy
required is E
E = -
E= -3.4 - (- 13.6)
E = 10.2eV
Therefore the bombarding particle must provide an energy of 10.2eV to excite the atom from n
=1 state to n=2 state
Similarly to excite the atom from n=1 state to n=3 state energy required is
E = - 1.51 – (-13.6)
E = 12.1eV
We say that first and second excitation energies of hydrogen are 10.2eV and 12.1eV respectively
(ii) EXCITATION POTENTIAL
Excitation potential is the minimum accelerating potential which provide an electron energy
sufficient to jump from the ground state n=1 to one of the outer orbits
Energy required to lift a electron from ground state n=1 to n=2 state is

Hence excitation potential for the first excited state of hydrogen is 10. 2V
Similarly energy required to lift an electron from ground state n=1 to n=2
The value of excitation potential depend upon the state to which the atom is excited to which the
atom is excited from the ground state
(iii) IONIZATION ENERGY
Ionization energy is the minimum energy needed to ionized an atom
Consider the case of hydrogen atom it has only one electron and this normally occupies the
ground state.
The energy of the electron for n= state is zero and if the electron is lifted to this level (n= ) it
becomes free of hydrogen atom i.e. hydrogen atom is ionized
(iv) IONIZATION POTENTIAL

Ionization potential is the minimum accelerating potential which would provide electron
energy sufficient to just remove the electron from the atom.
The ionization potential of one electron atom or ion is given by
(v) QUANTIZATION OF ENERGY
Quantization of energy is the existence of energy radiated by atoms in a specific amount which
is are integral multiples of a constant (hf).
SUCCESS OF BOHR’S THEORY
The success of bohr's theory is not to be attributed so much to the mechanical picture of atom he
proposed but rather to the development of mathematical explanation that agrees exactly with
experimental observations. Bohr’s theory achieved the following successes.
i) MADE ATOM STABLE
Bohr’s theory made the atom stable according to this theory an electron moving in the formatted
(quantum) orbits cannot lose energy even though under constant acceleration. This provided
stability to the atom.
ii) INTRODUCED QUANTUM MECHANICS
Bohr’s theory introduced quantum mechanics in the realm of atom for the first time
Bohr’s explained that sub- atomic particles e.g. electrons are governed by the laws of quantum
mechanics and not by classical laws of electron hydrogen as assumed by Rutherford
This completely changed our thinking and was the major step towards the discovery of the
rudiment laws of the atomic world
iii) GAVE MATHEMATICAL EXPLANATION OF HYDROGEN SERIES

The hydrogen series found by various scientists were based on empirical relation but had no
mathematical explanation
However these relations were easy derived by applying Bohr Theory
Further the size of hydrogen atom as calculated from this theory agreed very closely with the
experimental value.
LIMITATIONS OF BOHR’S THEORY
Bohr’s simple theory of circular orbits inspire of its many successes was found inadequate to
explain many phenomena observed experimentally.
This theory suffered from the following drawbacks.
(i) It could not explain the difference in the intensities of emitted radiations.
(ii) It is silent about the wave properties of electron
(iii) It could not explain experimentally observed phenomena such as Zeeman Effect,
Stack effect etc.
(iv) Bohr’s model does not explain why the orbit are circular while elliptical path is
also possible
(v) It could only partially explain hydrogen atom. For example this theory does not
explain the fine structure of spectral lines in the hydrogen atom
WORKED EXAMPLES
1. 1. Find the radius of the first orbit of hydrogen atom. What will be the velocity of electron in
the first orbit? Hence find the size of hydrogen atom
Solution
The radius of nth orbit of it atom is given by
Radius of first orbit of it atom n=1

Velocity of electron in the nth orbit of hydrogen atom is given by
=
Velocity of electron in the first orbit of hydrogen atom is given by
Since there is one electron in hydrogen atom the size hydrogen atom is equal to double the radius
of the first orbit
Size of the atom
= 2
= 2 x 0.53Å

Size of an atom =1.06Å
2 2. (a) The hydrogen atom is stable in the ground, state why?
(b) The ionization energy of hydrogen is 13. 6eV what does it mean?
(c) Calculate the wavelength of second line of Lyman series
Solution
If the hydrogen atom is in the ground state (n=1) there is no state of lower energy to which a
down ward transition can occur thus a hydrogen atom in the ground state is stable
a) It means that energy required to remove the single electron from the lowest energy
state of hydrogen atom to becomes free electron is 13.6eV
b) Second line of Lyman series is obtained when electron jumps from third orbit
=3 to the first orbit n=1
According to Bohr’s theory the wavelength of emitted radiation is given by
=
=
= x
3 3.( a) What is the meaning of negative energy of orbiting electron?
(b) What would happen if the electron in atom were stationary?

Solution
a) The negative total energy means that it is bound to the nucleus. If it acquires enough energy
from some external source (a collision for example) to make its total energy zero the electron is
no longer bound it is free.
b) If the electrons were stationary they would fall into the nucleus due to electrostatic force of
attraction so atom would be unstable i.e. it would not exist
c) For Paschen series we have longest wavelength line =4
This is a wavelength in the infrared part. Other lines in this series have shorter wavelength
bad approach series limit of wavelength to given by This wavelength is also in the hydrogen part.
This the range or centre series (820.4nm to 1875nm) is the infrared
4. a) If an electron jumps from first orbit to third orbit will it absorb energy?
b) Name the series of hydrogen spectrum lying in the infrared region
c) Calculate the shortest wavelength of the Balmer series
d) What is the energy possessed by an electron for n=?
Solution
a) Yes it is because the energy level of third orbit is more than that of the first orbit
b) * Paschen series
* Bracket series
* P fund series
Solution
In Balmer series the radiation of shortest wavelength (i.e. of highest of highest energy) is emitted
when electron jumps from infinity orbit = to the second orbit =2 of hydrogen atom.
5 5. a) The ionization potential of hydrogen is 13.6V what does it mean?
b) Find the longest wavelength in Lyman series
c) How much is the ionization potential of hydrogen atom?
d) The energy of the hydrogen atom in the ground state is 13.6eV. Determine the energies of
those energy levels whose quantum numbers are 2 and 3.
Solution
a) The ionization energy of hydrogen is 13.6eV. Therefore, if an electron which has been
accelerated from rest through a p.d of 13.6V collides with a hydrogen atom it has exactly the
right amount of energy to produce ionization.

This is a common method of producing ionization and therefore the term ionization potential is
often used.
b) Solution
In Lyman series the radiation of longest wavelength (i.e. lowest energy) is emitted when electron
jumps from second orbit =2 to first orbit n=1 of hydrogen atom
c) The energy of hydrogen atom in the ground state is – 13.6eV. therefore its ionization energy is
13.6eV and ionization potential =13.6V
d) Solution
The energy of an electron in the nth orbit of hydrogen atom is given by
6
6. a) Name the series of hydrogen spectrum lying in the
i) Visible region
ii) Utraviolet region of electromagnetic spectrum
b) Write the empirical relation for Paschen series lines of hydrogen spectrum
c) What are the values of first and second excitation potential of hydrogen atom?
d) Calculate the radii and the energy of three lowest energy allowed orbits for the electron in
Lithium ion. What is the energy of a photon that when absorbed causes an electron in
Lithium ion to be excited from n=1 to n=3 state?

Solution
a) i) Balmer series
ii) Lyman series
b) The wavelength of the spectral lines in paschen series are given by
c) Excitation energy for first excited state = -3.4 – (-13.6)
=10.2eV
For second excited state
= - (1. 51 - (-13.6)
= 12.1eV
Solution
d) (I ) for a single electron atom or ion the radius of the nth orbit is given

For a single electron atom or ion the energy of electron in the nth orbit is given by
Thus the energy of n=1, 2 and 3 orbits. The photo energy must be equal to the energy needed to
excite the electron
E3 – E1 =hf

(-13.6) – (-122.4) =photon’s energy
Photon’s energy = 108.8eV
7. The ionization energy of hydrogen like atom is 4rydbergs
(a) What is the wavelength of radiation emitted when electron jumps from first
excited state to the ground state?
(b)What is the radius of the first orbit for this atom?
(d) According to Bohr’s theory what is the angular momentum of a electron in the
third orbit
Solution
The energy electron in the nth orbit of hydrogen like atom is

The energy required to excite the electron from n=1 level to n=2
If is the wavelength of the emitted radiations then, Radius of first orbit for this atom
Solution
( b) Radius of nth orbit

(c) Solution
Angular momentum L of an electron in nth orbit is
L = n
Here n=3
Then
L= 3
L=
7 8. The energy levels of an atom are shown in figure below.

(a)Which one of these transitions will result in the emission of photon of wavelength 275nm?
(b) An electron orbiting in hydrogen atom has energy level of 3.4eV what will be its angular
momentum
(c) The total energy of an electron in the first excited state of hydrogen atom is about
– 3. 4eV what is the wavelength?
solution
(a) Energy of emitted photon E
Therefore photon of wavelength 275nm will be emitted for transition B
Solution

(d) K.E of electron = -(total energy of electron)
K.E of electron =3.4eV
ii) P.E of electron = 2xtotal energy
P.E of electron = -6.8eV
10. (a) How many lines can be drawn the energy level diagram of hydrogen atom?
(b) Use Bohr's model to determine the ionization energy of the He ion also calculate the
minimum wavelength a photo must have to cause ionization
(d) i) In neon atom the energies of the 3s and 3p states are respectively 16.70eV and
18.70eV. What wavelength corresponds to 3p -3s transitions in neon atom?
ii) The wavelength of the first member of the Balmer series in hydrogen spectrum is
6563Å. Calculate the wavelength of first member of Lyman series in the same spectrum
PLANCK’S QUANTUM THEORY OF BLACK BODY RADIATION
The findings in the black body radiation led Max plank in 1901 to postulate that radiant energy is
quantized i.e. it is radiated in form of energy packets.
BASIC POSTULATES OF THE PLANK’S THEORY
1. Any radiation is associated with energy.
2. Radiant energy is emitted or absorbed in small packets known as quanta.
3. The energy associated with a quantum is proportional to the frequency f of the radiation

4. The energy is absorbed or emitted only in whole number of quanta
Black Body Radiation
A blackbody is a substance that absorbs all light fall on it and does not reflect any light.
It is not easy to get a black body however a sealed metal box with a very small hole on it is very
close to a black body.
From law of physics it follows that a good absorber of radiation also is a good radiator. A black
body is supposed to be the best radiator.
When a black body is heated it emits light. The colour of light emitted changes from red to
yellow then to white as the temperature is increased.
The change in colour with temperature shows that the frequency changes with temperature.
This in contradiction with the classical wave theory since in the classical wave theory energy is
uniformly distributed over the wave form when heating the black body the colour of radiation
should stay the same
Only the intensity is supposed to increase with temperature.
DISTRIBUTION OF ENERGY IN THE SPECTRUM OF A BLACK BODY
Lamer and Pringshein investigated the distribution of energy amongst the different wavelength
of a thermal spectrum of a back body radiation

The results obtained by Lamer and Pringshein are shown in figure below
Results:
1. At a given temperature the energy is not uniformly distributed in the radiation
spectrum of a hot body
2. At a given temperature the intensity of radiations increases with increased in
wavelength and at a particular wavelength λ its value is maximum with further
increase in wavelength the intensity of heat radiations decreased
3. With increase in temperature wave length increases, wavelength emission of energy
takes place.
The points on the dotted line represent wavelength at various temperatures
4. For all wavelength an increase in temperature causes an increase in the energy
emission The area under each curve represents the total energy emitted for the
complete spectrum at a particular temperature
5. This area increases in temperature of the body. It is found that the area is directly
proportional to fourth power of the temperature of the body
This represents Stefan’s Boltzmann’s law.

Plank’s constant
Plank's constant is a fundamental constant equal to the ratio of the quantum energy to the
frequency of the radiation.
ELECTRON EMISSION
This is the liberation of electron from the surface of a substance.
For electron emission metals are used because they have many free electrons.
If a piece of metal is investigated at room temperature the random motion of free electrons is as
shown in figure below
However these electrons are free only to the extent that they may transfer from one atom to
another within the metal but they cannot leave the metal surface to provide electron emission.
It is because the free electron that start at the surface of metal find behind them positive nuclei
pulling them back and none pulling forward.
This at the surface of a metal a free electron encounters force that prevents it to leave the metal
In other words the metallic surface offers a barrier to free electrons and is known as surface
barriers
However if sufficient external energy is given to the free electron its kinetic energy is increased
and thus electron will cross over the surface barrier to leave the metal.
WORK FUNCTION OF THE METAL

This is the additional energy required by an electron to overcome the surface barrier of the metal.
Or
This is the minimum energy required by an electron to just escape from the metal surface.
The work function depends on
i) Nature of metal
ii) Conditions of the metal surface
It is measured by a smaller unit of energy called electron volt. (eV) because this is the
conventional unit of energy i.e. joule is very large for computations in atomic and nuclear
physics.
Electron volt.
One electron volt is the amount of energy acquired by an electron when it is accelerated through
a potential difference of IV
Since potential difference V
Work done = QV
For an electron
The electron volt is the kinetic energy gained by an electron being accelerated by a potential
difference of one volt.

The work function of pure metal varies roughly from V to V as shown in table below
Metal Work Function Wo (eV)
Cs 2.14
K 2.30
Na 2.75
Ca 3.20
Mo 4.17
Pb 4.25
Al 4.28
Hg 4.49
Cu 4.65
Ag 4.70
Ni 5.15
Pt 5.65
It is clear from the table above that the work function of platinum is the highest while it is lowest
for Cesium.
It is desirable that metal used for electron emission should have low work function so that a
small amount of energy is required to cause emission of electrons
PHOTOELECTRIC EFFECT
Photoelctric effect is the phenomenon of emission of electron from a metallic surface when
radiation of suitable frequency falls on it or is the phenomenon where electromagnetic radiation
of certain frequency when incident on certain material liberates electron from the surface of the
material.
Photo emission
Photo emission is the emission of electron by electromagnetic radiation.
Photo electrons
These are emitted or rejected electrons from the surface of the cathode.
Photo electric effect is a general phenomenon exhibited by all substances but is most easily
observed with metals.
When radiation of suitable frequency the threshold frequency is incident on a metallic surface
electrons are emitted from the metal surface.

The threshold frequency is different for metals.
Certain alkali, metals e.g. sodium potassium, calcium show photo electric effect when visible
light falls on them.
However, metal like zinc, calcium, magnesium etc show photo electric effect to ultra violet light.
Threshold Frequency
The threshold frequency is the minimum frequency of the incident radiation which is just
sufficient to eject photo electron from surface of a metal Or is the minimum frequency of
radiation below which no photo electron emission occurs.
It is denoted by
Illuminating a metal surface with light of frequency less than will not cause ejection of photo
electrons, no matter now great is the intensity of radiation.
But illumination with a frequency greater than causes emission of photo electrons even if
the radiation intensity is very small
Threshold wavelength
The threshold wavelength is the maximum wavelength of the incident radiation at which photo
electric emission occurs.
It is the wavelength corresponding to threshold frequency
If the wavelength of the incident radiation is greater than threshold wavelength then there will be
no photo electric emission.
Photoelectric current is the photo-electrons emitted per second
EXPERIMENTAL STUDY OF PHOTO ELECTRIC EFFECT
Figure below shows the experimental set up for studying the photoelectric effect.

The arrangement consists of an evacuated glass or quartz tube inclusive a photosensitive cathode
C and metallic A.
A transparent window W is sealed onto the glass tube which can be covered with different filters
to obtain the desired frequency.
The anode and cathode are connected to a battery through a potential divided by which potential
difference between anode and cathode can be changed.
The reversing switch RS tends to make anode positive or negative with respect to cathode.
The P.D between anode and cathode is measured by the voltmeter V while photoelectric current
is indicated by the micro ammeter.
1.
1.Effect of intensity of light on photo electric current
The anode A is maintained at positive potential with respect to cathode C and a radiation of
suitable frequency (above threshold frequency) is incident on cathode C.
As a result photo electric current is set up.
Keeping the frequency of incident radiation and accelerating potential fixed the intensity of the
incident radiation is changed in steps.
For each value of intensity of radiations the corresponding value of photo electron current is
noted.
If we plot a graph between intensity of radiation and photoelectric current it is found to be a
straight line passing through the origin O as shown in figure below

This shows that photoelectric current is directly proportional to the intensity of incident radiation
The intensity of radiation can be changed by changing the distance between cathode C and the
source of radiation.
Effect of potential of anode with respect to cathode on photoelectric current
We keep the anode at some positive accelerating potential with respect to cathode C and
illuminate the cathode with radiation of fixed frequency f above threshold frequency and fixed
intensity I
If we increase the positive potential on anode gradually, it is found that photo electric current
also increases a stage comes when the photo electric current becomes maximum.
If we increase the positive potential on anode further the photo electric current does not increase.
This maximum value of photo electric current is called saturation current and corresponds to the
photo electrons emitted by the cathode reach the anode A

Now saturation current is of higher value as shown in figure below
This is expected because the greater the intensity of incident radiation the greater is the photo
electric current
Stopping potential
Stopping potential is the minimum retarding potential at which photoelectric current becomes
zero Or is the potential difference when no electrons are able to reach the anode.
It is also known as stopping voltage or cut-off potential.
Stopping potential is a measure of the maximum kinetic energy of the photo electrons.
Since potential difference V
For stopping Voltage Vo

For an electron
At V0, even the photo electrons having maximum kinetic energy K.E max (i.e. fastest photo
electrons) cannot reach the anode A.
Therefore, the stopping potential V0 is a measure of the maximum kinetic energy K.E max of the
photo electrons.
eV0 is the work done by the retarding force to stop the photo electron with maximum
kinetic energy and is therefore equal to K.Emax.
At V0, it is found that the photoelectric current cannot be obtained even if we increase the
intensity of radiation. It is same for different intensities I1, I2 and I3 of incident radiation.
3. Effect of frequency of incident radiation on stopping potential.
We now study the relation between the frequency f of the incident radiation and the stopping
potential V0.
For this purpose, we take the radiations of different frequencies but of the same intensity.
For one frequency say f1, of the incident radiation, we plot the graph between photoelectric
current and potential of anode A with respect to cathode C at a constant intensity of incident
radiation
Keeping the intensity of incident radiation the same, we repeat the experiment for frequency f2
of the incident radiation.

The following is the resulting graph
Observations from the graphs
1. The value of stopping potential is different from radiation of different frequencies
2. The value of stopping potential is move in low higher frequency. This implies that the value of
maximum kinetic energy depend on the frequency of incident radiation.
The greater the frequency of incident radiation, the greater is the kinetic energy of emitted photo
electrons.
3. The value of saturation current depends on the intensity of incident radiation but is
independent of the frequency of incident radiation.
If we draw a graph between the frequency of incident radiation (f) and the stopping potential
(V0) at constant intensity of radiation, it will be a straight line AB as shown in figure below

From the graph
At fo, stopping potential V0 = 0. It means that at fo, the photo electric current is just zero (i.e.
photo electrons and emitted with zero velocity) and there is no retarding potential.
V0 = 0
This limiting frequency fo is called threshold frequency for the cathode material.
It is a minimum frequency of the incident radiation which is just sufficient to eject photo
electrons (i.e. with zero velocity) from the surface of a metal.
Stopping potential is directly proportional to the frequency of incident radiation.
V0 α f
The greater the frequency of incident radiation, the higher is the stopping potential and vice
versa.

Experiments show that photo electric emission is an instantaneous process.
As soon as light of suitable frequency (equal to or greater than fo) is incident on the surface of
the metal, photo electrons are emitted from the metal surface.
The time delay is less than 10-9 second
LAWS OF PHOTOELECTRIC EMISSION
The above experimental study of photoelectric effect leads to the following laws of photoelectric
emission.
i. For a given metal, there exists a certain minimum frequency of incident radiation below
which no emission of photo-electrons takes place. This cut off frequency is called threshold
frequency fo.
ii. For a given metal and frequency of incident radiation (>fo) the photo electric current is
directly proportional to the intensity of incident radiation.
iii. Above the fo, the maximum kinetic energy of the emitted photo-electron is independent of the
intensity of the incident radiation but depends only upon the frequency of the incident radiation.
iv. The photoelectric emission is an instantaneous process.
The above laws of photoelectric emission cannot be explained on the basis of light or radiation.
This gave death blow to the wave theory of light or radiation.
FAILURE OF WAVE THEORY/CLASSICAL PHYSICS TO EXPLAIN
PHOTOELECTRIC EFFECT
The wave theory of radiation failed to explain photoelectric effect. This will become clear from
the following discussion.
I. According to wave theory of radiation the greater the intensity of the wave the
greater the energy of the wave.
So wave theory does explain why the number of emitted photoelectrons increase as the
intensity of radiation is increased.
But it fails to explain the experimentally observed fact that the velocity or kinetic energy of
the emitted photoelectron is independent of the intensity of incident radiation.
According to the wave theory, an increasing in the intensity of radiation should increase the
kinetic energy of the emitted photoelectrons but it is contrary to the experimentally observed
fact.

II. According to wave theory, intensity of radiation is independent of it is frequency it depends
upon the amplitude of electric field vector.
Therefore, an increase in the frequency of radiation should not affect the velocity or kinetic
energy of the emitted electrons.
But it is observed experimentally that if the frequency of the incident radiation is increased,
the kinetic energy of the emitted electrons also increases.
III. According to the wave theory, electrons should always be emitted from a metal by radiation
of any frequency if the incident been is strong enough.
However experiments show that no matter how great is the intensity of the incident radiation;
no electrons are emitted from the metallic surface if the frequency of radiation is less than a
particular value i.e. threshold frequency.
IV. According to the wave theory the energy of radiation is spread continuously over the wave
fronts of the radiation.
Therefore, a single electron in the metal will intercept only a small fraction of the wave’s
energy.
Consequently considerable time should be needed for an electron to absorb enough energy
from the wave to escape the metal surface.
But experiment show that electron are emitted as soon as radiation of suitable frequency
falls on the metallic surface.
In other words photoelectric emission is instantaneous there is no delay.
The above discussion is a convincing proof of the inability of the wave theory to explain the
photoelectric effect.
EINSTEIN QUANTUM THEORY OF LIGHT
Einstein explained photoelectric effect on the basis of Planck’s quantum theory.
According to Einstein light radiation consist of tiny packets of energy called quanta.
Photon
Photon is the single quantum of light radiation which travels with the speed of light.

The energy of a photon is given by E.
E=hf
where
f –frequency of light radiation
h – Plank’s constant.
Further, Einstein assumed that one photon of suitable frequency (=fo or >fo) can eject only one
photoelectron from the metal surface.
He suggested that the energy of a single photon cannot be shared among the free electron in the
metal.
Only one electron can absorb the energy of a single photon.
EINSTEIN’S PHOTOELECTRIC EQUATION
According to Einstein, one photoelectron is emitted from a metal surface if one photon of
suitable frequency is incident on the metal.
Suppose a photon of suitable frequency f (< than the fo for the metal) is incident on the metal.
The energy hf of the photon is spent in two ways

I. A part of photon energy is used in liberating the least tight bound electron from the metal
surface which is equal to the work function W0 of the metal.
II. The rest of the energy of photon appears as maximum kinetic energy of the emitted
electron.
Einstein summarized this idea in what is called the Einstein photoelectric equation.
Photon = work function + maximum kinetic energy
The above equation is known as Einstein’s photoelectric equation
If the frequency of the incident radiation is fo then the emitted photoelectron will have zero
velocity.
Maximum kinetic Energy of emitted photoelectrons is
If f < fo, then from above equation K.Emax is negative which is impossible therefore,
photoelectrons emission cannot occur if the frequency of incident radiation is less than fo.
If f > fo, then equation above K.Emax α f. This means that max kinetic energy of photoelectrons
depends only on the frequency (f) of the incident radiation.

NUCLEAR
PHYSICS
RADIOACTIVITY
This is the emission of radiations from heavily elements such as uranium whose nuclei are
unstable.
Radiations emitted are called alpha , Beta (β) particles and gamma rays.
RATE OF DISINTEGRATION
The number of atoms of radioactive elements disintegrating per second is directly
proportional to the number of atom present at that instant.
Where λ = decay constant
The negative sign (-) indicates that N decreases as time (t) increases.
If N0 is the number of atoms at time t= 0 and N is the number of atoms at time t. then:-
HALF LIFE

The half life time of a radioactive element is the times taken for the atoms disintegrate to
half their initial number.
NECTA 1994/1/19
Draw a graph of
SOLUTION:
This is the graph of radioactive decay in time.

X-RAYS
X-rays are produced by bombarding a target of heavy metal with high energy electron.
NECTA 1984/2/8
The emission of X-rays may be regarded as the inverse of photo electric effect.Explain
SOLUTION
X-Rays which are waves are produced by bombarding a hard metal with
electrons(particles)where as in photoelectric effect electron(particles) are liberated from ametal
surface by incident radiation(waves)
MODERN X-RAY TUBE

Electron are obtained from the filament by thermionic emission and are accelerated to the anode
having small target of high melting point such as tangstem.
X-RAY QUANTITY
Refers to the intensity of X-rays which increases with the number of electrons limiting the
target.This depends on the cathode temperature controlled by the heating current
X-RAY QUALITY
Refer to the penetrating power of X-ray and determined by velocity whith which electrons
strikes the target.
SOFT X-RAY:
Are those which can penetrate soft objects such as flesh
HARD X-RAY
Are those which can vibrate much more solid material

PROPERTIES OF X-RAY
1.They travel in a straight line.
2.They readily penetrate matter.
3.They affect photographic plates
4.They are not deflected by electric or magnetic field,because they have no charge
They are wave of wavelength 10A
X-RAY SPECTRA
CONTINUOUS SPECTRUM
Explained by electromagnetic theory.

It is due to electrical interaction between the bombarding electrons and the nuclei of the target
atom
An electron approaching a positively charged nucleus is accelerated and according to
electromagnetic theory accelerated motion is accompanied by emission of radiations in this case
x-ray
DISCRETE SPECTRA
These are explained by quantum theory.They are produced when the incident electron interact
with electron close to nucleus of the target atom.The bombarding electrons knock off electron in
their orbits and the created gaps are filled by electrons in the high energy levels,when they
moves in these gaps they produce x-ray photon.
The cut off wavelength or short wave limit(λ min)
This is the minimum wavelength of x-radiations which corresponds to the maximum energy of
the X-rays produced by electrons which have given out all their K.Æ• on a single encounter
with the target nucleus
ENERGY OF X – RAY:
Energy of an electron striking the atom of the target is eV where e = electronic charge.
V = p.d across the X-ray tube.
If a direct collision is made with a target atom and the energy is absorbed then on quantum
theory X-rays produced hence a maximum energy hV
Therefore
eV = 1/2mV2 = hV
eV = hc/ λ minimum

λmin = hc/eV
NECTA 1989/1/18
Calculate the wavelength of most energetic X-rays produced by a tube operating at 1.0 x 105V.
USES OF X – RAYS
1.in investigation of suspected bone fractures
2.Detection of lung tuber culosis (feased tissue is denser than a heatthy one).
3.Treatment of cancer (cancer cells are killed by X-rays)
4.Casting and welding joints can be inspected for internal imperfection.
5.It is used in the study of crystal structure refer to Bragg’s law.
NUCLEAR FISSION FUSSION
Nuclear fission is a splitting disintegrating of heavy nucleus such as uranium into two other
lighter nuclei (with several neutrons)
Example:

Nuclear fusion
This is the combination of light nuclei to form a heavier nucleus.
Example:
NECTA 1990/2/8

(1)Both fission and fusion are source of energy
Explain.
SOLUTION:
Fission-During disintegration of heavy nucleus such as uranium, energy is released which is
transformed into K.E of fragments.
Fussion-When light nuclei are fused together a large amount of energy is released in term of
heat.(eg
in the sun)

ATOMIC PHYSICS

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